Details

sample37.0ms

Algorithm

intervals

Results

17.0ms	81×	body	1280	valid
6.0ms	138×	body	80	valid
4.0ms	25×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.5b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
8.0ms	(/ 1.0 (hypot 1.0 x))
68.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
83.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2309	463
3	5002	463

prune129.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	4	79

Merged error: 13.9b

Counts

79 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.7b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r/` `associate-/r` `associate-/l*` `add-log-exp`
4×	`associate--l+`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `sqrt-div` `div-exp` `clear-num` `frac-sub` `flip--` `div-inv`
1×	`flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip-+`

Counts

4 → 85

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
34.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify39.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	299	576
1	1026	547
2	5001	544

prune206.0ms

Filtered

97 candidates to 70 candidates (72.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 13.9b

Counts

101 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
0.7b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
20.6b	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
8×	`pow1`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-*r/` `add-log-exp`
4×	`cube-div` `associate--l+` `div-inv`
3×	`sub-neg` `pow-unpow` `cbrt-div`
2×	`distribute-rgt-in` `cube-mult` `flip3--` `distribute-lft-in` `sqrt-pow1` `sqrt-div` `unpow3` `pow-exp` `frac-sub` `flip--` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `flip3-+` `pow1/2` `pow1/3` `diff-log` `div-exp` `pow-prod-down` `sqrt-prod` `rem-cbrt-cube` `flip-+`

Counts

4 → 119

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
5.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

series144.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
35.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
6.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

simplify70.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	506	901
1	2170	797
2	5002	789

prune225.0ms

Filtered

131 candidates to 68 candidates (51.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	132	3	135

Merged error: 13.9b

Counts

135 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
0.6b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `times-frac`
8×	`add-exp-log` `associate-*r/` `add-cbrt-cube`
6×	`add-log-exp`
4×	`flip3-+` `associate-*l/` `frac-sub` `flip-+`
3×	`flip3--` `associate-r` `associate-l` `associate-/r` `flip--` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `sqrt-div` `pow-prod-down` `associate--r+`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-exp` `prod-exp` `clear-num` `sqrt-prod` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
20.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series139.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (hypot 1.0 x))
69.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
25.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
36.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify80.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	533	882
1	2698	815
2	5001	815

prune298.0ms

Filtered

92 candidates to 68 candidates (73.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	91	4	95

Merged error: 13.9b

Counts

95 → 4

regimes93.0ms

Accuracy

0% (0.2b remaining)

Error of 15.4b against oracle of 15.2b and baseline of 15.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	63
1	75	63
2	80	63
3	80	63

end0.0ms

sample1.0s

Algorithm

intervals

Results

588.0ms	2781×	body	1280	valid
152.0ms	4055×	body	80	valid
110.0ms	656×	body	640	valid
37.0ms	318×	body	320	valid
14.0ms	190×	body	160	valid

Details

sample37.0ms

simplify11.0ms

prune2.0ms

localize7.0ms

rewrite24.0ms

series186.0ms

simplify69.0ms

prune129.0ms

localize12.0ms

rewrite21.0ms

series115.0ms

simplify39.0ms

prune206.0ms

localize18.0ms

rewrite27.0ms

series144.0ms

simplify70.0ms

prune225.0ms

localize23.0ms

rewrite42.0ms

series139.0ms

simplify80.0ms

prune298.0ms

regimes93.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling